I am wondering if there's a way to set up the author sorting so that for my fanfiction library, the author_sort_copy_method is 'copy' and for my other library, the author_sort_copy_method is 'invert'.
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Is that possible?

If running the same install of calibre, no it's not possible. However if you run one library via Calibre portable and the other through a basic install you should be able to accomplish what you want. Of course you can only run one at a time.